I started making a Rhombicosidodecahedron model from cherry wood, cut out pieces on my CNC machine and made some jigs to hold the pieces to get the bevel angles cut. I assembled the pieces and discovered that very small errors create problems! The triangle pieces seem to be the main culprit, I guess I need to start refining my technique a bit. Cutting the pieces on the CNC machine was the most time consuming, doing the bevels went pretty quick using the jigs, just a lot of repetitive cuts (while making sure not to get bitten by the saw).

I have found a simple solution to build polyhedra in wood. Buy a simple Machinest protractor. These can be accurately set to 2' minutes or arch or 1/30th of a degree. Use this to set a table saw blade. I have done it and it works great. Grissley has a protractor for about $50. Get the one with the dial. There are more accurate ones on ebay.

Have you tried gluing the plywood polygons together? Might need reinforcing strips behind each joint, pre-glued to one polygon like tabs on a paper model. Those would also need to be carefully profiled with the right angle.